Bring 3 cups each chicken broth and water to a boil with half teaspoon salt. Slowly stir in 1 1/4 cup polenta. Reduce the heat to low and cook, stirring one minute.

Cover and cook, stirring occasionally, until thickened, about 35 minutes. Whisk in up to 1 cup water until creamy. Stir in 1/2 pound chopped fontina and 2 tablespoons grated Parmesan until melted.